Solution:
Given the graphs (a) and (b)
a) The function of graph (a) is
[tex]f(x)=-4\sqrt{x+3}+1[/tex]
The graph of the function is shown below
Translating it to get the graph of
[tex]y=f(x)+4[/tex]
The translated function becomes
[tex]\begin{gathered} y=f(x)+4 \\ y=(-4\sqrt{x+3}+1)+4 \\ y=-4\sqrt{x+3}+1+4 \\ y=-4\sqrt{x+3}+5 \end{gathered}[/tex]
The translated graph is
b) The function of graph (a) is
[tex]g(x)=-|x|[/tex]
The graph of the function is shown below
Translating it to get the graph of
[tex]y=g(x-2)[/tex]
The translated function becomes
[tex]\begin{gathered} y=g(x-2) \\ y=-|x-2| \end{gathered}[/tex]
The translated graph is
